Topologically protected braiding in a single wire using Floquet Majorana modes

TL;DR

This paper demonstrates a method to achieve topologically protected braiding of Majorana modes within a single driven quantum wire by exploiting Floquet engineering and quasienergy states, eliminating the need for a 2D network.

Contribution

It introduces a novel approach to realize Majorana braiding in a single wire using Floquet topological superconductors and quasienergy modes, expanding the possibilities for quantum computing architectures.

Findings

Successfully simulates braiding of Majorana modes in a single wire

Shows Floquet systems can host zero and pi Majorana modes simultaneously

Provides a protocol for adiabatic exchange of Majorana modes using Floquet engineering

Abstract

Majorana zero modes are a promising platform for topologically protected quantum information processing. Their non-Abelian nature, which is key for performing quantum gates, is most prominently exhibited through braiding. While originally formulated for two-dimensional (2d) systems, it has been shown that braiding can also be realized using one-dimensional (1d) wires by forming an essentially two-dimensional network. Here, we show that in driven systems far from equilibrium, one can do away with the second spatial dimension altogether by instead using quasienergy as the second dimension. To realize this, we use a Floquet topological superconductor which can exhibit Majorana modes at two special eigenvalues of the evolution operator, 0 and pi, and thus can realize four Majorana modes in a single, driven quantum wire. We describe and numerically evaluate a protocol that realizes a topologically protected exchange of two Majorana zero modes in a single wire by adiabatically modulating the Floquet drive and using the pi modes as auxiliary degrees of freedom.